A saturable inductor, together with a shunt capacitor, may be used to dramatically reduce the width of a voltage or current pulse, as was observed by Peterson in 1946, by Melville in 1950, by Williams in 1954, and by other early workers in the field. For certain applications, other desirable features of such a voltage or current pulse or train of pulses include: (1) reduction of pulse rise time and fall time to a small fraction of the overall pulse width (e.g., ten percent or less); (2) production of high energy pulses (e.g., 0.1-10 MeV); and (3) provision of pulse repetition frequencies up to ten kilohertz. The subject invention provides saturable reactor and transformer apparatus that manifests these features.